cp's OEIS Frontend

A336932 The 2-adic valuation of A003973(n), the sum of divisors of prime shifted n.

%I A336932 #12 Jul 05 2022 23:30:48
%S A336932 0,2,1,0,3,3,2,3,0,5,1,1,1,4,4,0,2,2,3,3,3,3,1,4,0,3,2,2,5,6,1,2,2,4,
%T A336932 5,0,1,5,2,6,2,5,4,1,3,3,1,1,0,2,3,1,2,4,4,5,4,7,1,4,2,3,2,0,4,4,3,2,
%U A336932 2,7,1,3,4,3,1,3,3,4,2,3,0,4,1,3,5,6,6,4,1,5,3,1,2,3,6,3,1,2,1,0,3,5,2,4,6
%N A336932 The 2-adic valuation of A003973(n), the sum of divisors of prime shifted n.
%H A336932 Antti Karttunen, <a href="/A336932/b336932.txt">Table of n, a(n) for n = 1..65537</a>
%H A336932 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A336932 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A336932 Additive with a(p^2e) = 0, a(p^(2e-1)) = A007814(1+A003961(p)) + A007814(e).
%F A336932 a(n) = A007814(A003973(n)).
%F A336932 a(n) = A336937(A003961(n)).
%F A336932 For all n >= 1, a(n) >= A295664(n).
%o A336932 (PARI) A336932(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); valuation(sigma(factorback(f)),2); };
%o A336932 (PARI)
%o A336932 A007814(n) = valuation(n, 2);
%o A336932 A336932(n) = { my(f=factor(n)); sum(i=1, #f~, (f[i, 2]%2) * (A007814(1+nextprime(1+f[i, 1]))+A007814(1+f[i, 2])-1)); };
%o A336932 (Python)
%o A336932 from math import prod
%o A336932 from sympy import factorint, nextprime
%o A336932 def A336932(n): return (~(m:=prod(((q:=nextprime(p))**(e+1)-1)//(q-1) for p,e in factorint(n).items()))& m-1).bit_length() # _Chai Wah Wu_, Jul 05 2022
%Y A336932 Cf. A000203, A000290 (positions of zeros), A003961, A003973, A007814, A295664, A336937.
%K A336932 nonn
%O A336932 1,2
%A A336932 _Antti Karttunen_, Aug 16 2020